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  <div class="section" id="numpy-fft-ifft2">
<h1>numpy.fft.ifft2<a class="headerlink" href="#numpy-fft-ifft2" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.fft.ifft2">
<code class="sig-prename descclassname">numpy.fft.</code><code class="sig-name descname">ifft2</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">s=None</em>, <em class="sig-param">axes=(-2</em>, <em class="sig-param">-1)</em>, <em class="sig-param">norm=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/fft/_pocketfft.py#L950-L1035"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.fft.ifft2" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the 2-dimensional inverse discrete Fourier Transform.</p>
<p>This function computes the inverse of the 2-dimensional discrete Fourier
Transform over any number of axes in an M-dimensional array by means of
the Fast Fourier Transform (FFT).  In other words, <code class="docutils literal notranslate"><span class="pre">ifft2(fft2(a))</span> <span class="pre">==</span> <span class="pre">a</span></code>
to within numerical accuracy.  By default, the inverse transform is
computed over the last two axes of the input array.</p>
<p>The input, analogously to <a class="reference internal" href="numpy.fft.ifft.html#numpy.fft.ifft" title="numpy.fft.ifft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifft</span></code></a>, should be ordered in the same way as is
returned by <a class="reference internal" href="numpy.fft.fft2.html#numpy.fft.fft2" title="numpy.fft.fft2"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fft2</span></code></a>, i.e. it should have the term for zero frequency
in the low-order corner of the two axes, the positive frequency terms in
the first half of these axes, the term for the Nyquist frequency in the
middle of the axes and the negative frequency terms in the second half of
both axes, in order of decreasingly negative frequency.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>a</strong><span class="classifier">array_like</span></dt><dd><p>Input array, can be complex.</p>
</dd>
<dt><strong>s</strong><span class="classifier">sequence of ints, optional</span></dt><dd><p>Shape (length of each axis) of the output (<code class="docutils literal notranslate"><span class="pre">s[0]</span></code> refers to axis 0,
<code class="docutils literal notranslate"><span class="pre">s[1]</span></code> to axis 1, etc.).  This corresponds to <em class="xref py py-obj">n</em> for <code class="docutils literal notranslate"><span class="pre">ifft(x,</span> <span class="pre">n)</span></code>.
Along each axis, if the given shape is smaller than that of the input,
the input is cropped.  If it is larger, the input is padded with zeros.
if <em class="xref py py-obj">s</em> is not given, the shape of the input along the axes specified
by <em class="xref py py-obj">axes</em> is used.  See notes for issue on <a class="reference internal" href="numpy.fft.ifft.html#numpy.fft.ifft" title="numpy.fft.ifft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifft</span></code></a> zero padding.</p>
</dd>
<dt><strong>axes</strong><span class="classifier">sequence of ints, optional</span></dt><dd><p>Axes over which to compute the FFT.  If not given, the last two
axes are used.  A repeated index in <em class="xref py py-obj">axes</em> means the transform over
that axis is performed multiple times.  A one-element sequence means
that a one-dimensional FFT is performed.</p>
</dd>
<dt><strong>norm</strong><span class="classifier">{None, “ortho”}, optional</span></dt><dd><div class="versionadded">
<p><span class="versionmodified added">New in version 1.10.0.</span></p>
</div>
<p>Normalization mode (see <a class="reference internal" href="../routines.fft.html#module-numpy.fft" title="numpy.fft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.fft</span></code></a>). Default is None.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">complex ndarray</span></dt><dd><p>The truncated or zero-padded input, transformed along the axes
indicated by <em class="xref py py-obj">axes</em>, or the last two axes if <em class="xref py py-obj">axes</em> is not given.</p>
</dd>
</dl>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>ValueError</strong></dt><dd><p>If <em class="xref py py-obj">s</em> and <em class="xref py py-obj">axes</em> have different length, or <em class="xref py py-obj">axes</em> not given and
<code class="docutils literal notranslate"><span class="pre">len(s)</span> <span class="pre">!=</span> <span class="pre">2</span></code>.</p>
</dd>
<dt><strong>IndexError</strong></dt><dd><p>If an element of <em class="xref py py-obj">axes</em> is larger than than the number of axes of <em class="xref py py-obj">a</em>.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="../routines.fft.html#module-numpy.fft" title="numpy.fft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.fft</span></code></a></dt><dd><p>Overall view of discrete Fourier transforms, with definitions and conventions used.</p>
</dd>
<dt><a class="reference internal" href="numpy.fft.fft2.html#numpy.fft.fft2" title="numpy.fft.fft2"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fft2</span></code></a></dt><dd><p>The forward 2-dimensional FFT, of which <a class="reference internal" href="#numpy.fft.ifft2" title="numpy.fft.ifft2"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifft2</span></code></a> is the inverse.</p>
</dd>
<dt><a class="reference internal" href="numpy.fft.ifftn.html#numpy.fft.ifftn" title="numpy.fft.ifftn"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifftn</span></code></a></dt><dd><p>The inverse of the <em>n</em>-dimensional FFT.</p>
</dd>
<dt><a class="reference internal" href="numpy.fft.fft.html#numpy.fft.fft" title="numpy.fft.fft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fft</span></code></a></dt><dd><p>The one-dimensional FFT.</p>
</dd>
<dt><a class="reference internal" href="numpy.fft.ifft.html#numpy.fft.ifft" title="numpy.fft.ifft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifft</span></code></a></dt><dd><p>The one-dimensional inverse FFT.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p><a class="reference internal" href="#numpy.fft.ifft2" title="numpy.fft.ifft2"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifft2</span></code></a> is just <a class="reference internal" href="numpy.fft.ifftn.html#numpy.fft.ifftn" title="numpy.fft.ifftn"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifftn</span></code></a> with a different default for <em class="xref py py-obj">axes</em>.</p>
<p>See <a class="reference internal" href="numpy.fft.ifftn.html#numpy.fft.ifftn" title="numpy.fft.ifftn"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifftn</span></code></a> for details and a plotting example, and <a class="reference internal" href="../routines.fft.html#module-numpy.fft" title="numpy.fft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.fft</span></code></a> for
definition and conventions used.</p>
<p>Zero-padding, analogously with <a class="reference internal" href="numpy.fft.ifft.html#numpy.fft.ifft" title="numpy.fft.ifft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifft</span></code></a>, is performed by appending zeros to
the input along the specified dimension.  Although this is the common
approach, it might lead to surprising results.  If another form of zero
padding is desired, it must be performed before <a class="reference internal" href="#numpy.fft.ifft2" title="numpy.fft.ifft2"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifft2</span></code></a> is called.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">ifft2</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">array([[1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j], # may vary</span>
<span class="go">       [0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],</span>
<span class="go">       [0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],</span>
<span class="go">       [0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]])</span>
</pre></div>
</div>
</dd></dl>

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